Question: First consider the expression for: Take the product of $-1$ and $x$ and add $7$. Now select the answer that matches the following: The sum of $-6$ and the product of $-6$ and that expression.
Solution: Let's break this problem into smaller and easier pieces. What is the product of $-1$ and $x$ $-1 \times x = \color{orange}{-x}$ What does adding $7$ to $-x$ do? $-1x$ $ + 7$ What is the quantity of $-6$ times that expression $-6 \times (-1x + 7) = \color{orange}{-6(-x+7)}$ What is the sum of $-6$ and $\color{orange}{-6(-x+7)}$ $-6(-x+7)$ $ - 6$ So the entire expression we're considering can be written as $-6(-x+7)-6$.